Question: Solve for $e$. $7(2e-1)-3=6+6e$ $e =$
Solution: We need to manipulate the equation to get $ e $ by itself. $\begin{aligned} 7(2e-1)-3 &= 6+6e \\\\ 14e-7 -3&= 6+6e~~~~~~~~~~\gray{\text{Distribute}}\\\\ 14e-10 &= 6+6e~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 14e-10{-6e} &= 6+6e{-6e} ~~~~~~~~~~\gray{\text{Subtract 6e from each side}}\\\\ 8e-10&=6 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ 8e-10{+10} &=6 {+10} ~~~~~~~~~~\gray{\text{Add 10 to each side}}\\\\ 8e &=16 ~~~~~~~~~~\gray{\text{Combine like terms}}\\\\ \dfrac{8e}{{8}}&= \dfrac{16}{{8}}~~~~~~~~~~\gray{\text{Divide each side by 8}} \\\\ e &= {2} ~~~~~~~~~~\gray{\text{Simplify}}\\\\ \end{aligned}$ The answer: $ e= { 2 }~~~~~~~~$ [Let's check our work!]